Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days?

Options

A. 55
B. 45
C. 30
D. 20

Answer

D

Explanation

Let grass at the beginning =g
Rate at which grass grows per day = r
Rate at which one cow eats grass per day = x and no. of cows to eat the grass in 96 days = n
The, According to the question
`g + 24r = 70 xx 24 xx x .....(i)`
` g + 60r = 30 xx 60 xx x ....(ii)`
` g + 96r =n xx 96 xx x... (iii) `
Subtracting (i) from (ii), we get
`60r - 24r = 1800x - 1680x`
or, `36r = 120x `
Subtracting (ii) from (iii), we get
` 96r - 60r = 96nx - 1800x `
or, `36r = x [96n - 1800] ... (v) `
Putting `36r = 120x `
from (iv) in (v), we get
`120x = x [96n - 1800] ` [From (iv)]
or, `120 = 96n - 1800 `
or, `96n = 1920 `
or `n = (1920)/(96) = 20`
Therefore, required number of Cows to eat the grass in 96 days = n = 20.